Finite Group DatabasebetaFinite Group Databasebeta| order | 2169 |
| isoclinism | isoclinic class of C241⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C241⋊C3 |
| unambiguous semidirect product | C241⋊C32 |
| unambiguous semidirect product | (C3×C241)⋊C3 |
| Fitting, socle | C3×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 723 |
249 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D241⋊C3, C3⋊(D241⋊C3), D3×C241⋊C3, … |
| maximal normal subgroup of | C3×D241⋊C3, C3⋊(D241⋊C3), D3×C241⋊C3, … |
| maximal quotient of | C2×C3×C241⋊C3, C3×C5×C241⋊C3, ΓL(1,𝔽8)×C241⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2169, 3);